Interview Q & A-there are limited points in a circle (the number must be an even number ), can we find a straight line without passing through any point and divide all the points into two halves?

Consider this problem from outside the circle.

Randomly find a straight line l that is separated from the circle, and then draw a straight line between each two points to mark the intersection with L (if parallel, ignore ), then start to rotate L with any unlabeled point on L as the center, then it is bound to rotate to a certain angle, the straight line L is just equal to all points.

Interview Q & A-there are limited points in a circle (the number must be an even number ), can I find a straight line without passing through any point and divide all the points into two halves?